I cannot speak to what Rita Mulchahy's definitions are but the PMBoK does not contain a definition of Variance Report in any way. It does discuss variance analyses as a technique to determine where you are against where you had planned to be. Therefore, you can infer that your variance analyses become part of your status report.
The PMBoK does reference work performance reports and then points to a status report and progress report as two examples. I think the main difference between a status report and progress report is that the former is based on a point in time, i.e., this is true now. A progress report differs because it would report what occurred over a period of time. If your project was transporting goods across a geographical area, your status report might say that you are located in this city, all vehicles are operational, all employees are well. Your progress report might read that over the past two weeks your vehicles covered 500 miles from the last progress report.
Your variance analysis might be included in both: your status report might say that you should have been in city B but only are in city A, with an unfavorable variance of 200 miles; your progress report might read, we planned on 400 miles since the last progress report but traveled 500, a favorable variance of 100 miles.
Then you would have your forecast report and your trend report. Your trend reports would be historical, looking at your metrics across many progress and status reports and your forecast report would be predictive, using your trending and variance analysis to predict where you will be in the next future reporting period.
In real-world projects, who cares what you call it. You'll choose to call it what will resonate best with those who are consuming the information and you will include in your reports what they need to hear and understand. But if you need to understand this to pass the PMP test, I would bounce what you read with Rita (a very excellent source) with the PMBoK.